。
I want you to come to my birthday party.
Literal
I [of-の] birthday party [to-に] come want-[explanatory-んだ].
~てほしい is the 'I want [you/someone] to do' construction — 来てほしい = 'want [you] to come.' It's an i-adjective form agreeing with the wanter's perspective. Distinct from ~たい (the wanter's own desire) — ~てほしい wants someone else to act. The んだ frames this as a request or explanation of the speaker's feelings.